Timeline for Discontinuous convolutions
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| Sep 1, 2010 at 2:47 | comment | added | Terry Tao | Well, one only needs the series here to converge almost everywhere, rather than pointwise, so I think we can escape the Baire class. The construction I had in mind had the f_n being concentrated near multiples of 1, then multiples of 1/2 (perhaps with the opposite sign to keep the partial sums bounded), then multiples of 1/4, and so forth, while becoming very rapidly narrower as one progresses, which should create a lot of oscillation at every scale, while still being absolutely summable in L^1 and thus convergent pointwise a.e. | |
| Sep 1, 2010 at 0:40 | comment | added | Ashutosh | If $f_n$ is a sequence of continuous functions whose sum converges pointwise to $f$ then isn't it true that the set of points of continuity of f is dense in reals? | |
| Aug 31, 2010 at 20:14 | history | answered | Terry Tao | CC BY-SA 2.5 |